Chapter 5 Review Problems — Forces and Newton’s Laws · 10/23/14’’’’’ Chapter’5’Review’Problems’—’ForcesandNewton’sLaws’ 1’ ... Newton’s&Second&Law&

10/23/14 Chapter 5 Review Problems — Forces and Newton’s Laws 1

Chapter 5 Review Problems — Forces and Newton’s Laws

Graph of velocity vs. time and Newton’s Second Law The graph in the next column represents the motion of a 1500-kg car over a 20-second interval.

a) Describe in words the motion of the car. b) During which interval(s) is the net force on the car

zero? c) During which time interval(s) is the net force on the car

not zero? d) During which time interval(s) is the car accelerating? e) What is the net force acting on the car on the interval

1. A→ B 2. B → C 3. C → D 4. D → E 5. E → F

Newton’s Second Law State Newton’s second law in words. Write an equation expressing the law. What is the difference between the terms “force” and “net force”? How does the sign of the force applied to an object compare with the sign of the acceleration? What is the difference between dynamic problems and static problems? Give an example of each. Two forces are applied to a 2-kilogram block on a frictionless horizontal surface as shown in the diagram. Calculate the acceleration of the block.

A staging that weighs 300 N supports two painters, one 250 N and the other 300 N. The tension on the left is 400 N. What is the tension on the right?

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Problems1. Calculate:

a. the weight of a 16-newton object in poundsb. the weight of a 7-pound object in newtonsc. the weight of a 3-kilogram object on Earth in newtons d. the mass in kilograms of an object that weighs 12 newtons on Earth

2. How does the inertia of a 200-kg object compare to the inertia of a 400-kgobject?

3. A constant force is applied to a cart, causing it to accelerate. If the mass ofthe cart is tripled, what change occurs in the acceleration of the cart?

4. If the net force acting on an object is tripled, what happens to its acceleration?5. On the planet of Venus, the acceleration due to gravity is 8.86 m/s2. What is

the mass of a man weighing 800 N on the surface of that planet?6. A 60-kilogram boy rolls downhill on a bicycle with a mass of 12 kilograms.

What net force is acting on the boy and his bicycle if he accelerates at a rateof 3.25 m/s2?

7. A young girl whose mass is 30 kilograms is standing motionless on a 2-kgskateboard holding a 7-kg bowling ball. She throws the ball with an averageforce of 75 N. a. What is the magnitude of her acceleration?b. What is the magnitude of the acceleration of the bowling ball?

8. On the planet Mercury, a person with a mass of 75 kg weighs 280 N. Whatis the acceleration due to gravity on Mercury?

9. As a baseball player strikes the ball with his bat, the 1-kg bat applies anaverage force of 500 N on the 0.15-kg baseball for 0.20 seconds. a. What is the force applied by the baseball on the bat?b. What is the acceleration of the baseball?c. What is the speed of the baseball at the end of the 0.2 seconds?

10. The graph in the next column represents the motion of a 1500-kg car over a20-second interval. During which interval(s) is the net force on the carzero?

11. Referring again to the graph, what force is being applied to the car duringinterval CD?

12. Two forces are applied to a 2-kilogram block on a frictionless horizontalsurface as shown in the diagram. Calculate the acceleration of the block.

13. The graph to the right represents theacceleration of an object as a function of theforce applied to the object. What is the mass ofthe object?

14. A 50-kg woman wearing a seat belt is travelingin a car that is moving with a velocity of 10 m/s.In an emergency, the car is brought to rest in0.50 seconds. What force does the seat belt exerton the woman so that she remains in her seat?

Applying your knowledge1. A bowling ball is positioned near the front of a stationary wagon. If the

wagon is suddenly pulled forward, the bowling ball appears to movebackwards in the wagon. Use each of Newton’s three laws to explain whatis actually happening to the wagon-ball system.

2. A 0.1 kilogram ball held at waist height is dropped and bounces back uptoward a student’s hand. Include all of the words from the chaptervocabulary list in describing the motion of the ball.

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11/15/07 12:00:41 PM

CHAPTER 2 MECHANICAL EQUILIBRIUM 27CHAPTER 2 MECHANICAL EQUILIBRIUM 27

ASSESS

Concept Summary ••••••

CHAPTER 2 MECHANICAL EQUILIBRIUM 27

40. A monkey hangs by a strand of rope and holds onto the zoo cage as shown. Since her arm holding the cage is horizontal, only the rope supports her weight. How does the ten-sion in the rope compare with her weight?

41. Why can’t the strong man pull hard enough to make the chain perfectly straight?

Think and Solve ••••••

42. Two vertical chains are used to hold up a 1000-N log. One chain has a tension of 400 N. Find the tension in the other chain.

43. Lucy Lightweight stands with one foot on one bathroom scale and her other foot on a second bathroom scale. Each scale reads 300 N. What is Lucy’s weight?

44. Harry Heavyweight, who weighs 1200 N, stands on a pair of bathroom scales so that one scale reads twice as much as the other. What are the scale readings?

45. The sketch shows a painter’s staging in mechanical equilibrium. The person in the middle weighs 250 N, and the tensions in both ropes are 200 N. What is the weight of the staging?

47. A staging that weighs 300 N supports two painters, one 250 N and the other 300 N. The reading in the left scale is 400 N. What is the reading in the right scale?

47. Two children push on a heavy crate that rests on a basement floor. One pushes hori-zontally with a force of 150 N and the other pushes in the same direction with a force of 180 N. The crate remains stationary. Show that the force of friction between the crate and the floor is 330 N.

48. Two children push on a crate. They find that when they push together horizontally with forces of 155 N and 187 N, respectively, the crate slides across the floor at a constant speed. Show that the force of friction be-tween the crate and the floor is 342 N.

More Problem-Solving PracticeAppendix F

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40. Tension in the rope is greater than her weight.

41. Chain tensions on both sides of the book must form a parallelogram with a resultant that equals the weight of the book. This can only occur if each side of the chain makes an angle to the horizontal.

Think and Solve 42. From SF 5 0, total upward tensions 5 weight of log.

400 N 1 tension in other chain 5 1000 N. Tension in other chain 5 1000 N 2 400 N 5 600 N.

43. If each scale reads 300 N, Lucy’s total weight 5 600 N.

44. 800 N on one, 400 N on the other

45. SF 5 0, upward forces are 400 N, and downward forces are 250 N 1 weight of staging. So staging weighs 150 N.

46. SF 5 0, upward forces are 400 N 1 tension in right scale, and downward forces are 250 N 1 300 N 1 300 N 5 850 N. Reading on the right scale is 450 N.

47. From SF 5 0, Sforces in one direction 5 Sforces in opposite direction. So, 150 N 1 180 N 5 force of friction 5 330 N in opposite direction to the children’s pushes.

48. Crate moves at constant speed in a straight line, so

SF 5 0. Sforces in one direction 5 Sforces in opposite direction. So, 155 N 1 187 N 5 force of friction 5 342 N in

opposite direction to the children’s pushes.

T e a c h i n g R e s o u r c e s

• Computer Test Bank• Chapter and Unit Tests

27

0012_cp09te_CH02.indd 270012_cp09te_CH02.indd 27 1/30/08 10:45:57 AM1/30/08 10:45:57 AM


Newton’s Third Law State Newton’s Third Law. If a small sports car collides head-on with a massive truck, which vehicle experiences the greater impact force? Which vehicle experiences the greater acceleration? Explain your answers. You and your little 6 year old cousin are wearing ice skates. You push off each other and move in opposite directions.

a) How does the force you feel during the push compare to the force your cousin feels? Explain.

b) How do your accelerations compare? Explain.

A young girl whose mass is 30 kilograms is standing motionless on a 2-kg skateboard holding a 7-kg bowling ball. She throws the ball with an average force of 75 N.

a) What is the magnitude of her acceleration? b) What is the magnitude of the acceleration of the bowling ball?

Friction and Spring Force Use the graph to the right to answer the following questions. The graph shows the relationship between the applied force and the force of friction.

a) What is the relationship between the forces at point A?

b) What is the relationship between the forces at point B?

c) What applied force is needed for the object to begin to slide? A dart of mass 0.100 kg is pressed against the spring of a toy dart gun as shown in the figure. The spring (with spring stiffness constant k = 250. N/m) is compressed 6.0 cm and released. If the dart detaches from the spring when the spring reaches its natural length (x = 0), what acceleration does the dart acquire?

The graph shows the force Fx that an archer applies to the string of a long bow versus the string’s displacement x. Drawing back this bow is analogous to stretching a spring. From the data in the graph determine the effective spring constant of the bow.

7. If the truck’s initial velocity were halved, whatwould be the truck’s skidding distance?

A. !x/4B. !xC. 2!xD. 4!x

Use the graph below to answer questions 8–9. Thegraph shows the relationship between the appliedforce and the force of friction.

8. What is the relationship between the forces atpoint A?

F. Fs = FappliedG. Fk = FappliedH. Fs < FappliedJ. Fk > Fapplied

9. What is the relationship between the forces atpoint B?

A. Fs, max = FkB. Fk > Fs, maxC. Fk > FappliedD. Fk < Fapplied

SHORT RESPONSEBase your answers to questions 10–12 on the infor-mation below.

A 3.00 kg ball is dropped from rest from the roof of abuilding 176.4 m high. While the ball is falling, a hori-zontal wind exerts a constant force of 12.0 N on the ball.

10. How long does the ball take to hit the ground?

11. How far from the building does the ball hit theground?

12. When the ball hits the ground, what is its speed?

Base your answers to questions 13–15 on the informa-tion below.

A crate rests on the horizontal bed of a pickup truck.For each situation described below, indicate the motionof the crate relative to the ground, the motion of thecrate relative to the truck, and whether the crate will hitthe front wall of the truck bed, the back wall, or neither.Disregard friction.

13. Starting at rest, the truck accelerates to the right.

14. The crate is at rest relative to the truck while thetruck moves with a constant velocity to the right.

15. The truck in item 14 slows down.

EXTENDED RESPONSE16. A student pulls a rope attached to a 10.0 kg wood-

en sled and moves the sled across dry snow. Thestudent pulls with a force of 15.0 N at an angle of45.0°. If mk between the sled and the snow is 0.040,what is the sled’s acceleration? Show your work.

17. You can keep a 3 kg book from dropping by push-ing it horizontally against a wall. Draw force dia-grams, and identify all the forces involved. How dothey combine to result in a zero net force? Will theforce you must supply to hold the book up be dif-ferent for different types of walls? Design a seriesof experiments to test your answer. Identify exactlywhich measurements will be necessary and whatequipment you will need.

151Forces and the Laws of Motion

For a question involving experi-mental data, determine the constants, variables, andcontrol before answering the question.

0

Fs, max

Fk

Kinetic regionStatic region

A B

Applied force

Fric

tiona

l for

ce

PROBLEMS 313

the angular frequency decrease. (e) Both the amplitude and the

angular frequency increase.

Section 10.4 The Pendulum

14. Five simple pendulums are shown in the drawings. The lengths

of the pendulums are drawn to scale, and the masses are either m or

2m, as shown. Which pendulum has the smallest angular frequency of

oscillation? (a) A (b) B (c) C (d) D (e) E

Section 10.5 Damped Harmonic Motion

16. An object on a spring is oscillating in simple harmonic motion.

Suddenly, friction appears and causes the energy of the system to be

dissipated. The system now exhibits ______. (a) driven harmonic

motion (b) Hooke’s-law type of motion (c) damped harmonic

motion

Section 10.6 Driven Harmonic Motion and Resonance

17. An external force (in addition to the spring force) is continually

applied to an object of mass m attached to a spring that has a spring

constant k. The frequency of this external force is such that resonance

occurs. Then the frequency of this external force is doubled, and the

force is applied to one of the spring systems shown in the drawing.

D

m

BA

2m

C

2m

E

2mm

With which system would resonance occur? (a) A (b) B (c) C

(d) D (e) E

Section 10.7 Elastic Deformation

18. Drawings A and B show two cylinders that are identical in all re-

spects, except that one is hollow. Identical forces are applied to each

cylinder in order to stretch them. Which cylinder, if either, stretches

more? (a) A and B both stretch by the same amount. (b) A stretches

more than B. (c) B stretches more than A. (d) Insufficient informa-

tion is given for an answer.

Section 10.8 Stress, Strain, and Hooke’s Law

20. A material has a shear modulus of 5.0 ! 109

N/m2. A shear stress

of 8.5 ! 106

N/m2

is applied to a piece of the material. What is the

resulting shear strain.

A B

DBA

2m

8k

4m

2k

6m

4k

3m

9k

5m

10k

C E

Note to Instructors: Most of the homework problems in this chapter are available for assignment via an online homework management program suchas WileyPLUS or WebAssign, and those marked with the icon are presented in WileyPLUS using a guided tutorial format that provides enhanced interactivity. See Preface for additional details.

Note: Unless otherwise indicated, the values for Young’s modulus Y, the shear modulus S, and the bulk modulus B are given, respectively, in Table 10.1, Table10.2, and Table 10.3.

ssm Solution is in the Student Solutions Manual.This icon represents a biomedical application.

www Solution is available online at www.wiley.com/college/cutnell

PROBLEMS

Section 10.1 The Ideal Spring and Simple Harmonic Motion

1. ssm A hand exerciser utilizes a coiled spring. A force of 89.0 N is

required to compress the spring by 0.0191 m. Determine the force

needed to compress the spring by 0.0508 m.

2. The graph shows the force

Fx that an archer applies to the

string of a long bow versus the

string’s displacement x. Drawing

back this bow is analogous to

stretching a spring. From the

data in the graph determine the

effective spring constant of

the bow.

3. In a room that is 2.44 m high, a spring (unstrained length " 0.30 m)

hangs from the ceiling. A board whose length is 1.98 m is attached to

the free end of the spring. The board hangs straight down, so that its

1.98-m length is perpendicular to the floor. The weight of the board

(104 N) stretches the spring so that the lower end of the board just

extends to, but does not touch, the floor. What is the spring constant

of the spring?

4. A person who weighs 670 N steps onto a spring scale in the bath-

room, and the spring compresses by 0.79 cm. (a) What is the spring

constant? (b) What is the weight of another person who compresses

the spring by 0.34 cm?

5. ssm A car is hauling a 92-kg trailer, to which it is connected by a

spring. The spring constant is 2300 N/m. The car accelerates with an

acceleration of 0.30 m/s2. By how much does the spring stretch?

6. A spring lies on a horizontal table, and the left end of the spring

is attached to a wall. The other end is connected to a box. The box is

pulled to the right, stretching the spring. Static friction exists between

the box and the table, so when the spring is stretched only by a small

amount and the box is released, the box does not move. The mass of

the box is 0.80 kg, and the spring has a spring constant of 59 N/m. The

coefficient of static friction between the box and the table on which it

rests is How far can the spring be stretched from its

unstrained position without the box moving when it is released?

!S " 0.74.

x (m)

Fx (N)

160

0.24

2762T_ch10_285-319.qxd 6/3/08 9:44 PM Page 313


Mass vs. Weight Explain the difference between mass and weight. State common units for each. What is the force of gravity on a person who has a mass of 80.0 kg? On the planet of Venus, the acceleration due to gravity is 8.86 m/s2. What is the mass of a man weighing 800 N on the surface of that planet? On the planet Mercury, a person with a mass of 75 kg weighs 280 N. What is the acceleration due to gravity on Mercury? Dynamic Problems The graph to the right represents the acceleration of an object as a function of the force applied to the object. What is the mass of the object?

A 50-kg woman wearing a seat belt is traveling in a car that is moving with a velocity of 10 m/s. In an emergency, the car is brought to rest in 0.50 seconds. What force does the seat belt exert on the woman so that she remains in her seat? A baseball player strikes the ball with his bat. The 1.0 kg bat applies an average force of 500. N on the 0.15 kg baseball for 0.20 s.

a) What is the force applied by the baseball on the bat? b) What is the acceleration of the baseball? c) What is the speed of the baseball at the end of the 0.2 seconds?

The free-body diagrams below show four ways that two different forces could be exerted on an object. In which diagram is the object in equilibrium?

A 60. kg cyclist is riding up a hill on a bicycle with mass of 12 kg. What net force is acting on the cyclist is she accelerates at 1.25 m/s2?

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1. Two horizontal forces, one 180.0 N and theother 200.0 N, are exerted in oppositedirections on a boat on a lake. What is thenet horizontal force on the boat?

A 380.0 N

B 200.0 N

C 180.0 N

D 20.0 N

Objective: 4.01Thinking Skill: Applying

2. Two dogs play tug-of-war with a rope toythat has a mass of 0.50 kg. If one dog pullson the toy with a force of 140.0 N, and theother dog pulls in the opposite directionwith a force of 138.0 N, what is thehorizontal acceleration of the toy?

A 9.8 m/s2

B 8.0 m/s2

C 4.9 m/s2

D 4.0 m/s2


3. What is the force of gravity on a person whohas a mass of 80.0 kg?

A 176 N

B 686 N

C 784 N

D 801 N


4. A 60.0-kg boy rides in an elevator thataccelerates upward at 1.80 m/s2. What is thenet force exerted on the boy?

A 9.8 N

B 108 N

C 480 N

D 588 N


5. The free-body diagrams below show fourways that two different forces could beexerted on an object.

In which diagram is the object inequilibrium?

A Diagram 1

B Diagram 2

C Diagram 3

D Diagram 4

Objective: 3.01Thinking Skill: Analyzing

F2 ! 100 N

F1 ! 100 N

F2 ! 100 NF1 ! 100 N

F1 ! 100 N F2 ! 200 NDiagram 4

F2 ! 100 NF1 ! 200 NDiagram 3

Diagram 2

Diagram 1

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Chapter 5 Review Problems — Forces and Newton’s Laws · 10/23/14’’’’’ Chapter’5’Review’Problems’—’ForcesandNewton’sLaws’ 1’ ... Newton’s&Second&Law&